There is a cat in a box. Also in the box is a radioactive atom, which, if it decays within a certain interval, will trigger a time machine that sends the cat back in time to kill its own grandfather while he was still a kitten. (Why the cat has such an irrational hatred of its grandfather I don't know. I never said it was a nice cat.)
Unless you open the lid, there is no way of knowing whether there has ever been a cat in the box at all.